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Spectral Invariants of Integrable Polygons

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Název: Spectral Invariants of Integrable Polygons
Autoři: Mårdby, Gustav, 1999, Rowlett, Julie, 1978
Zdroj: Journal of Fourier Analysis and Applications. 31(6)
Témata: Polygonal billiard, Helmholtz equation, Zeta-regularized determinant, Laplace eigenvalues, Closed geodesic, Polygonal domain, Heat trace, Laplace spectrum, Spectral zeta function
Popis: An integrable polygon is one whose interior angles are fractions of π; that is to say of the form π n for positive integers n. We consider the Laplace spectrum on these polygons with the Dirichlet and Neumann boundary conditions, and we obtain new spectral invariants for these polygons. This includes new expressions for the spectral zeta function and zeta-regularized determinant as well as a new spectral invariant contained in the short-time asymptotic expansion of the heat trace. Moreover, we demonstrate relationships between the short-time heat trace invariants of general polygonal domains (not necessarily integrable) and smoothly bounded domains and pose conjectures and further related directions of investigation.
Popis souboru: electronic
Přístupová URL adresa: https://research.chalmers.se/publication/549109
https://research.chalmers.se/publication/549109/file/549109_Fulltext.pdf
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  Data: Spectral Invariants of Integrable Polygons
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Mårdby%2C+Gustav%22">Mårdby, Gustav</searchLink>, 1999<br /><searchLink fieldCode="AR" term="%22Rowlett%2C+Julie%22">Rowlett, Julie</searchLink>, 1978
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  Data: <i>Journal of Fourier Analysis and Applications</i>. 31(6)
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  Data: <searchLink fieldCode="DE" term="%22Polygonal+billiard%22">Polygonal billiard</searchLink><br /><searchLink fieldCode="DE" term="%22Helmholtz+equation%22">Helmholtz equation</searchLink><br /><searchLink fieldCode="DE" term="%22Zeta-regularized+determinant%22">Zeta-regularized determinant</searchLink><br /><searchLink fieldCode="DE" term="%22Laplace+eigenvalues%22">Laplace eigenvalues</searchLink><br /><searchLink fieldCode="DE" term="%22Closed+geodesic%22">Closed geodesic</searchLink><br /><searchLink fieldCode="DE" term="%22Polygonal+domain%22">Polygonal domain</searchLink><br /><searchLink fieldCode="DE" term="%22Heat+trace%22">Heat trace</searchLink><br /><searchLink fieldCode="DE" term="%22Laplace+spectrum%22">Laplace spectrum</searchLink><br /><searchLink fieldCode="DE" term="%22Spectral+zeta+function%22">Spectral zeta function</searchLink>
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  Data: An integrable polygon is one whose interior angles are fractions of π; that is to say of the form π n for positive integers n. We consider the Laplace spectrum on these polygons with the Dirichlet and Neumann boundary conditions, and we obtain new spectral invariants for these polygons. This includes new expressions for the spectral zeta function and zeta-regularized determinant as well as a new spectral invariant contained in the short-time asymptotic expansion of the heat trace. Moreover, we demonstrate relationships between the short-time heat trace invariants of general polygonal domains (not necessarily integrable) and smoothly bounded domains and pose conjectures and further related directions of investigation.
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      – Type: doi
        Value: 10.1007/s00041-025-10202-6
    Languages:
      – Text: English
    Subjects:
      – SubjectFull: Polygonal billiard
        Type: general
      – SubjectFull: Helmholtz equation
        Type: general
      – SubjectFull: Zeta-regularized determinant
        Type: general
      – SubjectFull: Laplace eigenvalues
        Type: general
      – SubjectFull: Closed geodesic
        Type: general
      – SubjectFull: Polygonal domain
        Type: general
      – SubjectFull: Heat trace
        Type: general
      – SubjectFull: Laplace spectrum
        Type: general
      – SubjectFull: Spectral zeta function
        Type: general
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      – TitleFull: Spectral Invariants of Integrable Polygons
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            NameFull: Rowlett, Julie
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              Type: published
              Y: 2025
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